Rewrite as a simplified fraction. ${0.\overline{81} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 81.8181...\\ 1x &= 0.8181...\end{align*}}$ Subtracting the two equations, we have: ${99x = 81}$ ${x = \dfrac{81}{99}} $ ${x = \dfrac{9}{11}} $